An object with a mass of #8 kg# is acted on by two forces. The first is #F_1= < -9 N , 2 N># and the second is #F_2 = < 6 N, -3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2018-01-31T15:11:13

The object's rate of acceleration is #=0.40ms^-2# in the direction #198.4^@# anticlockwise from the x-axis.

The resultant force is

#vecF=vecF_1+vecF_2 = <-9,2> + <6,-3> #

#= <-3, -1>#

The mass of the object is #m=8kg#

#vecF=mveca#

The acceleration is

#veca=1/mvecF=1/8* <-3, -1> = <-3/8, -1/8>#

The rate of acceleration is

#||veca||= ||<-3/8, -1/8>|| = sqrt((-3/8)^2+(-1/8)^2)#

#=sqrt(9/64+1/64)#

#=1/8sqrt10#

#=0.40ms^-2#

The direction is

#theta=180^@+arctan(1/3)=180+18.4=198.4^@# anticlockwise from the x-axis.